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avatar+1481 

In parallelogram DEFG, the difference between two adjacent angles is 32 degrees. Which is the measure of the larger angle?

 

A. 96 degrees

B. 114 degrees

C. 106 degrees

D. 118 degrees

 

 

 

In a regular pentagon ABCDE and regular hexagon MNOPQR, 2AB = 3MN and CD + QR = 10. Which is 4BC + 5PQ?

 

A. 44

B. 33

C. 42

D. 38

 Jan 15, 2020
 #1
avatar+107405 
+3

First one

 

In a parallelogram, two adjacent angles  sum to 180°

 

So

 

x  + (x - 32)  =  180

 

2x - 32  =  180         add 32 to both sides

 

2x  =   212                divide both sides by  2

 

x  = 106°

 

cool cool cool

 Jan 15, 2020
 #2
avatar+107405 
+3

Let the  side of the pentagon  = x  and the side of the hexagon  =  y

 

2AB  = 3MN

CD  + QR    = 10   ......so.....

 

2x  = 3y

x  +  y  =  10  

 

2x  - 3y    =  0

x    +  y  =  10              multtiply  the second equation by 3

 

2x  -  3y  =  0

3x   + 3y   = 30          add these

 

5x  =  30

x  = 6

And y  = 4

 

So

 

4BC + 5PQ  =

 

4(6) + 5(4)  =

 

24  +  20  =

 

44

 

 

cool cool cool

 Jan 15, 2020

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